The last two properties together ensure that a coherent risk metric will also be convex.
The risk metric that we adopt in this paper is informed from cumulative prospect theory [1]}, and is not coherent.
Human players or operators have been known to demonstrate a preference to play safe with gains and take risks with losses.
Further, they tend to deflate high probability events, and inflate low probability events.
Cumulative prospect theory (CPT) is a risk measure that has been empirically shown to capture human attitude to risk [1]}, [3]}.
This risk metric uses two utility functions \(u^+\)  and \(u^-\) , corresponding to gains and losses, and weight functions \(w^+\)  and \(w^-\)  that reflect the fact that value seen by a human subject is nonlinear in the underlying probabilities [4]}.
